40 MODERN SEISMOLOGY 
these are adopted as the surface values. For greater distances 
we have to abandon the supposition that the velocities are con- 
stant throughout the earth, but this point we postpone to a 
later chapter and meanwhile retain the hypothesis of uni- 
formity. 
The boundary of the earth introduces many new features 
in the seismogram to be observed at a station, over and above 
those which we have mentioned and which will be referred to 
briefly as P and S. 
Following Huygens’ principle, each point of the spherical 
disturbances (V, and V,) spreading out from the focus will, as 
it reaches the earth’s surface, become a centre from which 
spread two spherical disturbances (V, 
and V,), so that we have on the seis- 
mogram a whole series of diffraction 
effects in addition to P and S. 
Let E represent the earthquake 
focus supposed to be near the surface, 
O the station, and C the centre of 
(i the earth. Further, let the earth’s 
Fi. 9. radius be R and the angular distance 
EO be @. Then the arc 
EO=4=R@ 
and chord EO = 2R sin 6/2. 
The first effect at O is the beginning of the longitudinal phase 
P at a time 
Z= 2h sin g 
1) WV a 
Now consider the disturbance which travels as a longitudinal 
disturbance V, by the path EA and then as a diffracted 
longitudinal disturbance V, by the path AO. It reaches the 
station at a time 
t= 7 (sin as sin 2) = - sin ; cos(=") 
These disturbances start immediately after P and arrive at 
later and later instants for 6, > or < @, until they culminate in 
the brachistochronic path of maximum time, which is also that 
of regular reflexion, when 6, = 6,. 
